Abstract: On an almost quaternionic manifold we study the integrability of almost complex structures which are compatible with the almost quaternionic structure . If , we prove that the existence of two compatible complex structures forces to be quaternionic. If , that is is an oriented conformal 4-manifold, we prove a maximum principle for the angle function of two compatible complex structures and deduce an application to anti-self-dual manifolds. By considering the special class of Oproiu connections we prove the existence of a well defined almost complex structure on the twistor space of an almost quaternionic manifold and show that is a complex structure if and only if is quaternionic. This is a natural generalization of the Penrose twistor constructions.